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RELATED APPLICATION DATA
This invention is related to application Ser. No. 08/643,115, filed Apr.
30, 1996, entitled "Encrypted Holographic Data Storage Based on Orthogonal
Phase Code Multiplexing," which is commonly assigned with the present
invention and is herein incorporated by reference.
FIELD OF THE INVENTION
The present invention relates to the field of holographic storage, and in
particular to a method of differential video image compression.
BACKGROUND OF THE INVENTION
Since the development of off-axis holography in the 1960's, volume
holography has been identified as a promising candidate for high density
data storage. Theoretically, up to 10.sup.14 bits of information can be
stored in 1 cm.sup.3 of a volume holographic medium. In addition,
holographic storage promises fast data transfer rates, estimated at over 1
Gb/s. For general information on holographic memory systems, see for
example the articles by Heanue et al. in Science 265: 749-752 (1994), Hong
et al. in Optical Engineering 34(8): 2193-2203 (1995), and Psaltis and Mok
in Scientific American 273(5): 70-78 (1995), or U.S. Pat. No. 4,927,220
(Hesselink et al.) and U.S. Pat. No. 5,450,218 (Heanue et al.).
One of the major challenges facing holographic data storage has been
increasing the capacity of storage systems. Several approaches have been
used for multiplexing, or storage of multiple pages within a system.
Typical approaches include spatial, angular and phase-code multiplexing.
For an overview of these techniques, see for example the above-mentioned
article by Hong et al.
Three major noise sources affect the performance of typical holographic
storage systems. Imperfections in detectors cause detector noise.
Imperfections in the medium structure cause undesired scatter, which is
independent on the number of pages stored in the system. Interpage
crosstalk leads to a reconstruction of undesired pages when the medium is
accessed with a reference beam corresponding to a given page. The
crosstalk-limited SNR (object signal intensity/crosstalk intensity) varies
inversely with the number of stored pages, for a fixed average intensity
per page. For a review of interpage crosstalk for angular and phase-code
multiplexing see for example the article by Bashaw et al. in J. Opt. Soc.
Am. B, 11: 1820-1836 (1994), herein incorporated by reference. Interpage
crosstalk is an important barrier facing efforts to increase the capacity
of holographic storage media.
OBJECTS AND ADVANTAGES OF THE INVENTION
In light of the above, it is a primary object of the present invention to
provide a method of increasing the effective capacity of crosstalk-limited
holographic storage devices for storing video images. It is another object
of the present invention to provide a method of encoding data in a video
holographic storage system that leads to reduced interpage crosstalk. It
is yet another object of this invention to provide compression and
decompression methods allowing fast optical decoding of stored pages.
These and other objects and advantages will become more apparent after
consideration of the ensuing description and accompanying drawings.
SUMMARY OF THE INVENTION
The present invention provides a method of storing video images {F›i!} as
pages {S›i!} in a holographic storage medium. A video image F›k! is
identified as a basis image and stored by recording a basis page S›k! in
the medium. A subsequent image F›k+n! is stored by recording in the medium
a page S›k+n!=F›k+n!-a›k!F›k!. Preferably, a›k! is a positive number on
the order of 1. More preferably, a›k! is substantially equal to 1.
In one embodiment, the subtraction operation need not be coherent, and is
performed electronically (pixel by pixel). In a preferred embodiment, the
subtraction operation is coherent. Coherent subtraction is understood to
mean a subtraction operation that allows recovering an image
F'›k+n!=F›k+n! by accessing the medium using a reference wave function
R›k+n!+b›k!R›k!, where R›k+n! corresponds to S›k+n! and R›k! corresponds
to S›k!. Coherent subtraction can be accomplished in several ways.
In one embodiment, a page S'›k+n!=F›k+n! is recorded using a reference wave
function R›k+n!, and a page S"›k+n!=a›k!F›k! is recorded using a reference
wave function R'›k+n!=R›k+n!exp(i.pi.). The component(s) of the reference
wave function R'›k+n! are identical in amplitude, but phase-shifted by
.pi., relative to those of R›k+n!. Then S›k+n! is recorded as
S'›k+n!-S"›k+n!=F›k+n!-a›k!F›k!, and S›k+n! corresponds to R›k+n!.
In another embodiment, a page S'›k+n!=F›k+n! is recorded using a reference
wave function R›k+n!, and a page S"›k+n!=a›k!F›k!exp(i.pi.) is recorded
using R›k+n!. That is, a phase delay of .pi. is introduced in the signal
beam path during the recording of S"›k+n!, relative to the recording of
S'›k+n!. Then S›k+n! is recorded as S'›k+n!-S"›k+n!=F›k+n!-a›k!F›k!, and
S›k+n! corresponds to R›k+n!.
In yet another embodiment, a digital page S.sup.+ ›k+n! is recorded using a
reference wave function R›k+n!. The digital page S.sup.+ ›k+n! contains a
positive part of a page F›k+n!-a›k!F›k!. Consider a digital image
comprising a collection of pixels. Denote by p›i,j! the value stored at
the jth pixel of the ith page. A positive part of F›k+n!-a›k!F›k! contains
values of the pixels p›j! for which the difference p›k+n,j!-a›k!p›k,j! is
positive. A digital page S.sup.- ›k+n! comprising a negative part of
F›k+n!-a›k!F›k! is then recorded using a reference wave function
R›k+n!exp(i.pi.). The page S›k+n! is thus recorded as S.sup.+
›k+n!+S.sup.- ›k+n!=F›k+n!-a›k!F›k!, and S›k+n! corresponds to R›k+n!.
In still another embodiment, a page F›k+n!-a›k!F›k! generated by coherent
subtraction is directly encoded into a signal beam through the use of a
compound phase-and-amplitude spatial light modulator. That is, S›k! and
S›k+n! specify amplitude and phase modulations imparted on reference
beams, rather than amplitude-only modulations as in conventional
recording. The phase modulation is used to specify the sign of the
difference between a value of a component p›k+n,j! of F›k+n! and a value
of a component a›k!p›k,j! of a›k!F›k!. In one embodiment, the
negative-difference components are phase-delayed by .pi. relative to the
positive-difference components.
In a preferred embodiment, the reference wave function R›k! specifies a
phase modulation imparted on a reference beam. In general, however, the
important requirement in a method of the present of the invention is that
R›k! be substantially orthogonal to R›k+n!. In an embodiment, R›k! and
R›k+n! specify amplitude and phase modulations. In another embodiment,
R›k! specifies an angle between a reference beam and the storage medium.
In a preferred embodiment, the basis image is reset whenever there is a
substantial difference between an image to be stored and the current basis
image. An average intensity I›k! of an image G›k!=F›k!-a›k-m!F›k-m! is
determined, where F›k-m! is an original or current basis page. If I›k!
exceeds a predetermined threshold T, F›k! is identified as a new basis
image and is stored as a page S›k!=F›k!. If I›k! is below T, F›k! is
stored as a page S›k!=F›k!-a›k-m!F›k-m!.
Preferably, the similarity verification process described above is repeated
for F›k+n!. An average intensity I›k+n! of an image G›k+n!=F›k+n!-a›k!F›k!
is determined, and F›k+n! is stored as a page S›k+n!=F›k+n!-a›k!F›k! if
I›k+n! is less than T, and as a page S›k+n!=F›k+n! if I›k+n! exceeds T.
A basis page is preferably marked by a basis signal comprising a part of a
page S›k-q!, where q is any integer. A basis signal contains a
predetermined set of data. In one embodiment, a basis signal comprises a
blank or checkerboard-patterned section of a page. In a preferred
embodiment, the basis signal comprises an entire page preceding a basis
page. In this embodiment, q=1 and the basis signal is the page S›k-1!
itself.
In a preferred embodiment, multiple pages are stored with reference to a
common basis page. That is, an image F›k+n+p! is stored as a page
S›k+n+p!=F›k+n+p!-a›k!F›k!.
In another embodiment, each page is stored with reference to its
predecessor. In this embodiment an image F›k+n+1! is stored as a page
S›k+n+1!=F›k+n+1!-a›k+n!F›k+n!. Differential encoding between consecutive
pages is useful in circumstances in which the accumulation of noise from
one page to the next is minimal.
A basis image F'›k! is retrieved by reading a basis page S›k! and assigning
F'›k!=S›k!. Subsequent images are retrieved as F'›k+n!=S›k+n!+b›k!S›k!,
where b›k!.noteq.0, and preferably b›k!=a›k!=1. Since time constraints are
crucial during decoding, the step of retrieving F'›k+n! preferably
comprises a coherent addition of S›k+n! and b›k!S›k!. The addition is
achieved by accessing the medium using a reference wave function
R›k+n!+b›k!R›k!.
If multiple pages are stored with reference to a common basis page, a page
F›k+n+p! originally stored as a page S›k+n+p!=F›k+n+p!-a›k!F›k! is
retrieved by reading S›k+n+p! and assigning F'›k+n+p!=S›k+n+p!+b›k!S›k!,
where b›k!=a›k!.
If each page is stored with reference to its predecessor, an image F›k+n+1!
originally stored as a page S›k+n+1!=F›k+n+1!-a›k+n!F›k+n! is retrieved by
reading S›k+n+1! and assigning
##EQU1##
where the coefficients b›k+j! are chosen such that F'›k+n!=F›k+n!, i.e.
##EQU2##
Preferably, b›k!=a›k!=1 for all k.
The present invention further provides a video image storage apparatus
comprising a storage identification means for identifying an image F›k! as
a basis image, and a storage means for recording a page S›k!=F›k! and a
page S›k+n!=F›k+n!-a›k!F›k!, where a›k!.noteq.0 and preferably a›k!=1. The
storage means comprises multiplexing means such as a phase-code,
phase-and-amplitude-code, angular multiplexing means, or other
monochromatic multiplexing means.
Preferably, the multiplexing means comprises a phase spatial
light-modulator for recording S›k! using a phase reference wave function
R›k!, and for recording S›k+n! using a phase reference wave function
R›k+n! such that R›k+n! is orthogonal to R›k!. In one embodiment, the
multiplexing means comprises compound phase-and-amplitude modulating means
placed in the reference beam path. In another embodiment, the multiplexing
means comprises angular multiplexing means for changing the orientation of
the reference beam relative to the signal beam and/or the storage medium.
Depending on the method used for the coherent subtraction of data pages,
the storage apparatus further comprises either an amplitude spatial light
modulator, or a compounds phase-and-amplitude spatial light modulator
placed in the signal beam. path.
Data is retrieved using a video image retrieval apparatus comprising a
retrieval identification means for identifying a page S›k! as a basis
page, and a retrieval means for retrieving a basis image F'›k!=S›k! and an
image F'›k+n!=S›k+n!+b›k!S›k!, wherein b›k!.noteq.0. The retrieval
identification means comprises either a table of basis pages, or a means
for determining an average intensities of S›k! and S›k+n!.
The apparatus preferably comprises a multiplexing means for reading S›k!
using R›k! and reading S›k+n! using R›k+n!+b›k!R›k!. In one embodiment,
the multiplexing means in the retrieval apparatus is identical to the
multiplexing means in the storage apparatus used to store S›k! and S›k+n!.
In an angle-multiplexed system, the readout multiplexing means comprises a
simultaneous angular multiplexing means for simultaneously accessing the
medium with two reference beam at different angles, one beam corresponding
to R›k+n!, and the other to b›k!R›k!.
A video compression method of the present invention leads to a reduction in
interpage crosstalk. In addition, the use of optical page-by-page addition
for retrieval allows fast readout and eliminates the need for a
time-consuming electronic decompression step.
DESCRIPTION OF THE FIGURES
FIG. 1-A shows a schematic perspective view of a setup for phase-code
mutiplexing images in a holographic storage medium, according to the
present invention.
FIG. 1-B is a schematic diagram of a system similar to that shown in FIG.
1-A.
FIG. 2-A shows two pixels of a PSLM having different associated phase
delays, used for the storage of an image.
FIG. 2-B shows two pixels of a PSLM having identical associated phase
delays.
FIGS. 3A-3H shows eight one-dimensional Walsh functions and their pixel
correspondents, according to the present invention.
FIG. 4 shows six rows of pixels corresponding to a wave function W.sub.m,
where adjacent rows are separated by a distance d, according to the
present invention.
FIG. 5-A illustrates the presence of Bragg selectivity in the horizontal
direction, according to the present invention.
FIG. 5-B illustrates the absence of Bragg selectivity between adjacent
codes in the vertical direction, according to the present invention.
FIG. 6-A shows two binary images and their coherent (phase and amplitude)
difference, according to the present invention.
FIG. 6-B shows two gray-scale images and their coherent (phase and
amplitude) difference, according to the present invention.
FIG. 6-C shows digital pages that comprise positive and negative parts of a
binary digital image.
FIG. 7-A is a simplified flowchart showing the encoding steps in a
preferred embodiment of the present invention.
FIG. 7-B shows the correspondence between images and recorded pages for a
sequence of images, according to a method of the present invention.
FIG. 8 shows two Walsh functions and their sum, according to the present
invention.
FIG. 9 is a simplified flowchart showing decoding steps in a preferred
embodiment of the present invention.
FIG. 10-A shows two binary images and their electronic (amplitude only)
difference, according to the present invention.
FIG. 10-B shows two gray-scale images and their electronic (amplitude only)
difference, according to the present invention.
DETAILED DESCRIPTION
In the following discussion, for some quantity A, the notation A›i! is
understood to correspond to some (fixed) i, while the notation {A›i!} is
understood to refer to a set of A›i! for varying values of i. The notation
S›i! is understood to refer to a wave function of a signal beam, or,
equivalently, to a modulation imparted on a signal beam by a spatial light
modulating means. The notation R›i! refers to a wave function/modulation
of a reference beam.
The statement that an image F›i! is stored in a medium is understood to
mean that a corresponding page S›i! is recorded in the medium. The page
S›i! contains information that is necessary, but that need not be
sufficient, for the recovery of F›i!. That is, in general S›i! need not be
identical to F›i!. The statement that a page S›i! is read is understood to
imply that the medium is accessed with a reference wave function that is
not orthogonal to R›i!, where R›i! is the wave function used for the
recording of S›i!. The statement that a page S›i! corresponds to a
reference wave function R›i! is understood to mean that accessing the
medium with R›i! results in a reconstruction of S›i!.
A method of the present invention is particularly suited for the
holographic storage of video images, i.e. images having some degree of
interimage similarity or correlation. Video images include real images and
transforms of real images, such as for example JPEG or other linear or
non-linear transforms of real images. In particular, video images include
real images having a moving foreground and a substantially constant
background. Eliminating the redundant storing of the background in
consecutive frames leads to a reduction in the average intensity of the
stored pages, and consequently to increased capacity in a
crosstalk-limited storage system.
The following discussion will address first multiplexed holography, and
thereafter electronic (non-coherent) and coherent coding and decoding of
video images in holographic media.
Multiplexed Holography
In a typical volume holographic storage system data is stored in a
photosensitive storage medium. Storage materials investigated so far
include photorefractive crystals, doped glasses, photorefractive polymers,
photopolymers, and bacteriorhodopsin. Suitable holographic storage media
are generally known in the art. Media comprising photorefractive crystals,
such as lithium niobate (LiNbO.sub.3) or strontium barium niobate (SBN),
have proved to be particularly useful for holographic storage.
Several approaches have been used for multiplexing, or storing of multiple
pages in a medium. Common approaches include spatial, wavelength, angular,
and phase-code multiplexing. In a method using electronic
subtraction/addition of data pages, any multiplexing approach is suitable.
For a method employing coherent subtraction and addition of data pages,
phase-code and angular multiplexing are suitable approaches. Since
phase-code recording and phase-and-amplitude readout are the preferred
approaches for coherent subtraction/addition, and can also be used with
electronic subtraction/addition, the following discussion will focus on
phase-code and phase-and-amplitude-code multiplexing. As is apparent to
the skilled artisan, however, the present invention can used with other
multiplexing approaches, and in particular with angular multiplexing.
Phase Code Multiplexing
Orthogonal phase code multiplexing offers a number of advantages over
angular and wavelength multiplexing, including the possibility of
implementation with fixed geometry and wavelength, and the possibility of
performing linear operations on the stored data by modulating the
reference beam. For further information on orthogonal phase-code
multiplexing, see for example U.S. Pat. No. 3,612,641, or articles by Denz
et al. in Opt. Comm. 85: 171 (1991), Taketomi et al. in Opt. Lett. 16:
1774 (1991), and Taketomi et al. in 1991 OSA Topical Meeting on
Photorefractive Materials, Effects, and Devices, Beverly, Mass., p. 126
(1991).
FIG. 1-A is a schematic perspective view of a holographic storage system
suitable for phase-code multiplexing. Information is recorded in a
recording medium 20 as an interference pattern produced by a reference
beam 22 and a signal beam 24. The interference pattern (grating)
corresponding to a data page is stored throughout medium 20. For readout,
only the reference beam is sent through the medium, and the interaction of
the reference beam with the stored grating yields a reconstruction of the
stored data.
A coherent light source such as a laser 26 generates a beam that is split
by a beam splitter 28 into reference beam 22 and signal beam 24. Beams 22
and 24 pass through the lenses 30 and the spatial light modulators (SLMs)
38, 40, and are reflected by the mirrors 44. Ways of arranging lenses and
mirrors for spatially manipulating and transforming beams are well known
in the art. In angle- and phase-code-multiplexed systems, reference beam
22 is preferably perpendicular to signal beam 24 within holographic medium
20, so as to minimize crosstalk due to Bragg-mismatched reconstruction. In
wavelength multiplexed systems, an arrangement in which reference beam 22
is counter propagating with signal beam 24 within medium 20 yields a
maximal wavelength selectivity.
If, as in a preferred embodiment, both phase and amplitude information is
encoded in the signal beam, SLM 38 is a compound phase-and-amplitude
spatial light modulator (PASLM). Similarly, in a preferred embodiment SLM
40 is a PASLM. If, as in a conventional phase-code-multiplexed storage
system, only amplitude information is encoded in the signal beam and only
phase information is encoded in the reference beam, SLM 38 is an amplitude
spatial light modulator (ASLM) and SLM 40 is a phase spatial light
modulator (PSLM).
In a preferred embodiment, medium 20, lenses 30, and SLMs 38, 40 are placed
in a Fourier arrangement. If the pixels of SLMs 38, 40 are approximated as
point sources, such a placement effectively Fourier transforms the pixels
of SLMs 38, 40 into plane wave components. As is apparent to the skilled
artisan, however, a Fresnel (i.e. non-Fourier) arrangement is also
suitable for holographic storage.
FIG. 1-B is a more detailed view of a Fourier system similar to that in
FIG. 1-A, showing beam expanders 46 and a camera 48. Camera 48 reads out
reconstructed data pages. In the embodiment shown in FIG. 1-B, reference
beam 22 is modulated by an ASLM 50 and a PSLM 52, while signal beam 24 is
modulated by an ASLM 54 and a PSLM 56.
In a preferred embodiment, the reference wave functions are two-level
(0-.pi.) functions. Multi-level phase functions are also suitable in a
method of the present invention, however, as long as the reference wave
functions are orthogonal. An intuitive understanding of phase-code
multiplexing can be achieved with reference to the two-element, two-level
phase functions illustrated in FIGS. 2-A and 2-B. Each element of a phase
function corresponds to a pixel p.sub.1 or p.sub.2 of SLM 38. The pixels
p.sub.1 and p.sub.2 alter the phase of light passing though them. The
hatching in FIG. 2-A refers to the phase, not amplitude, modulation
imparted by the pixels. In FIG. 2-A, the phase of light passing through
p.sup.(A).sub.1 is unaltered, while the phase of light passing through
p.sup.(A).sub.2 is modified by .pi.. In FIG. 2-B, the phase of light
passing through p.sup.(B).sub.1 and p.sup.(B).sub.2 is unaltered.
Consider a page S stored with the phase function shown in FIG. 2-A.
Accessing the recording medium with the same phase function results in a
reconstruction of S. The signal component reconstructed using
p.sup.(A).sub.1 interferes constructively with the signal component
reconstructed using p.sup.(A).sub.2. The constructive interference of the
signal components results in the reconstruction of S at the detector.
Accessing the medium with the phase function shown in FIG. 2-B, however,
will result in a zero net signal, since the signal reconstructed using
p.sup.(B).sub.2 will be out of phase with the signal reconstructed using
p.sup.(B).sub.1. The net output signal is therefore zero. A second page S'
is then stored using the phase function in FIG. 2-B. Accessing the
recording medium with the phase function in FIG. 2-A results in a
reconstruction of S, while accessing the medium with the phase function in
FIG. 2-B results in a reconstruction of S'.
Two-level orthogonal phase code multiplexing is an extension of the above
example to a set of orthogonal phase functions having N elements. If any
two functions in the orthogonal set are compared, half the elements will
be different and half the elements will be the same between the two
functions. Suppose an image is stored using one of the N-element phase
functions. If readout is performed with a different (orthogonal) N-element
phase function, the signals reconstructed with the N/2 elements that are
the same as in the original function will interfere destructively with the
signals reconstructed with the N/2 elements that are different. Thus,
accessing the medium with any function orthogonal to the function used to
store a given image will not result in the reconstruction of that image.
In a preferred embodiment, the orthogonal functions used for multiplexing
are Walsh functions. For more information on Walsh functions, see for
example K. G. Beauchamp, Applications of Walsh and Related Functions,
Academic Press, London, 1984. The application of orthogonal Walsh
functions to phase-code multiplexed holographic storage is also described
in the above-mentioned U.S. Pat. No. 3,612,641.
Sets of N-element Walsh functions can be constructed for arbitrary values
of N. Constructing sets of Walsh functions is well known in the art, and
can be done for example by linearly combining Rademacher functions
sign›sin(2.sup.n .pi.x)!. FIGS. 3A-3H shows eight one-dimensional Walsh
functions, and corresponding pixel representations, where pixel colors
refers to phase (not amplitude) modulations. In general, there are N
distinct orthogonal functions in a set of N-element Walsh functions. For
two arbitrary different functions in a set, exactly N/2 pixels are
identical in the two functions, and exactly N/2 pixels are different
between the two functions.
In a preferred embodiment, the multiplexing functions are one-dimensional
Walsh functions, rather than two-dimensional ones.
That is, the wave function corresponds to rows of pixels, rather than to a
two-dimensional array of pixels. FIG. 4 shows several rows of pixels
separated by a distance d. Preferably, the set of rows in a page of PSLM
38 comprises a Walsh function. It is also possible for each row to
represent a Walsh function. The crucial requirement, for crosstalk
purposes, is only that the functions {R›j!} be orthogonal.
For clarity, in the following discussion the plane defined by the reference
beam and the signal beam is understood to be the horizontal plane. The
preference for a one-dimensional reference wave function is due to the
fact that in phase-code multiplexed systems, there is Bragg selectivity in
the horizontal, but not vertical direction, as illustrated below.
Consider two pixels p and p', adjacent on a row of PSLM 40. If the pixels
are approximated as points, the reference beam will have a plane wave
component with a wave vector .rho. corresponding to p, and a plane wave
component with a wave vector .rho.' corresponding to p'. Consider a signal
beam having plane wave components with wave vectors denoted collectively
.sigma., where it is understood that the orientations of .sigma. span a
range, as shown in the k-space diagrams of FIG. 5-A. For simplicity, the
orientations of .sigma. are shown to vary only within the horizontal
plane. FIG. 5-A also shows grating vectors collectively denoted K,
recorded by the interference of the signal beam and the part of the
reference beam corresponding to pixel p. A second set of grating vectors
K' is recorded by the interference of the signal beam and the part of the
reference beam corresponding to pixel p'. Note that the gratings
corresponding to p and p' are recorded in distinct, non-overlapping
regions in k-space.
Consider now two closely-spaced pixels p and p", adjacent on a column of
PSLM 40. Consider a signal beam having plane wave components .sigma. whose
orientations span ranges in the horizontal and vertical directions, as
shown in the k-space diagrams of FIG. 5-B. The grating K corresponding to
p is recorded in a region of k-space overlapping with that used to record
the grating K" corresponding to p". That is, if a page S is stored using
only pixel | | |
